Random Space Filling

Author(s): John Shier, Paul Bourke (iVEC@UWA)
Description: Iterative space filling of the plane with non-overlapping and non-Apollonian shapes has applications to problems in packing, geology, and pure mathematics. If on each iteration the area is reduced by some monotonically decreasing function then there appears to be only one such function that ensures space filling, namely the Reimann Zeta function. The behavour has been experimentally verified for multiple shapes and in dimensions 1, 2, and 3. Space filling has been confirmed irrespective of the complexity of the shape, and even for variable shapes.